Internal problem ID [14559]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.3, page 156
Problem number: 53.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }+6 y^{\prime }+25 y=-1} \] With initial conditions \begin {align*} \left [y \left (0\right ) = -{\frac {1}{25}}, y^{\prime }\left (0\right ) = 7\right ] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 16
dsolve([diff(y(t),t$2)+6*diff(y(t),t)+25*y(t)=-1,y(0) = -1/25, D(y)(0) = 7],y(t), singsol=all)
\[ y \left (t \right ) = \frac {7 \,{\mathrm e}^{-3 t} \sin \left (4 t \right )}{4}-\frac {1}{25} \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 22
DSolve[{y''[t]+6*y'[t]+25*y[t]==-1,{y[0]==-1/25,y'[0]==7}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {7}{4} e^{-3 t} \sin (4 t)-\frac {1}{25} \]